Modeling dynamic demand response using Monte Carlo simulation and interval mathematics for boundary estimation

With the rapid development of various technologies and applications in smart grid implementation, demand response has attracted growing research interests because of its potentials in enhancing power grid reliability with reduced system operation costs. This paper presents a new demand response model with elastic economic dispatch in a locational marginal pricing market. It models system economic dispatch as a feedback control process, and introduces a flexible and adjustable load cost as a controlled signal to adjust demand response. Compared with the conventional “one time use” static load dispatch model, this dynamic feedback demand response model may adjust the load to a desired level in a finite number of time steps and a proof of convergence is provided. In addition, Monte Carlo simulation and boundary calculation using interval mathematics are applied for describing uncertainty of end-user's response to an independent system operator's expected dispatch. A numerical analysis based on the modified Pennsylvania-Jersey-Maryland power pool five-bus system is introduced for simulation and the results verify the effectiveness of the proposed model. System operators may use the proposed model to obtain insights in demand response processes for their decision-making regarding system load levels and operation conditions.

Science, ICT and Mathematics Education in Rural and Regional Australia: The SiMERR National Survey

The SiMERR National Survey was one of the first priorities of the National Centre of Science, Information and Communication Technology and Mathematics Education for Rural and Regional Australia (SiMERR Australia), established at the University of New England in July 2004 through a federal government grant. With university based ‘hubs’ in each state and territory, SiMERR Australia aims to support rural and regional teachers, students and communities in improving educational outcomes in these subject areas. The purpose of the survey was to identify the key issues affecting these outcomes. The National Survey makes six substantial contributions to our understanding of issues in rural education. First, it focuses specifically on school science, ICT and mathematics education, rather than on education more generally. Second, it compares the different circumstances and needs of teachers across a nationally agreed geographical framework, and quantifies these differences. Third, it compares the circumstances and needs of teachers in schools with different proportions of Indigenous students. Fourth, it provides greater detail than previous studies on the specific needs of schools and teachers in these subject areas. Fifth, the analyses of teacher ‘needs’ have been controlled for the socio-economic background of school locations, resulting in findings that are more tightly associated with geographic location than with economic circumstances. Finally, most previous reports on rural education in Australia were based upon focus interviews, public submissions or secondary analyses of available data. In contrast, the National Survey has generated a sizable body of original quantitative and qualitative data.

Tutoring with higher mathematics and the use of technology

We discuss three approaches to the use of technology as a teaching and learning tool that we are currently implementing for a target group of about one hundred second level engineering mathematics students. Central to these approaches is the underlying theme of motivating relatively poorly motivated students to learn, with the aim of improving learning outcomes. The approaches to be discussed have been used to replace, in part, more traditional mathematics tutorial sessions and lecture presentations. In brief, the first approach involves the application of constructivist thinking in the tertiary education arena, using technology as a computational and visual tool to create motivational knowledge conflicts or crises. The central idea is to model a realistic process of how scientific theory is actually developed, as proposed by Kuhn (1962), in contrast to more standard lecture and tutorial presentations. The second approach involves replacing procedural or algorithmic pencil-and-paper skills-consolidation exercises by software based tasks. Finally, the third approach aims at creating opportunities for higher order thinking via "on-line" exploratory or discovery mode tasks. The latter incorporates the incubation period method, as originally discussed by Rubinstein (1975) and others.

A playful side to twelfth-century mathematics

As editors of the book Lilavati's Daughters: The Women Scientists of India, reviewed by Asha Gopinathan (Nature 460, 1082; 2009), we would like to elaborate on the background to its title. Lilavati was a mathematical treatise of the twelfth century, composed by the mathematician and astronomer Bhaskaracharya (1114–85) — also known as Bhaskara II — who was a teacher of repute and author of several other texts. The name Lilavati, which literally means 'playful', is a surprising title for an early scientific book. Some of the mathematical problems posed in the book are in verse form, and are addressed to a girl, the eponymous Lilavati. However, there is little real evidence concerning Lilavati's historicity. Tradition holds that she was Bhaskaracharya's daughter and that he wrote the treatise to console her after an accident that left her unable to marry. But this could be a later interpolation, as the idea was first mentioned in a Persian commentary. An alternative view has it that Lilavati was married at an inauspicious time and was widowed shortly afterwards. Other sources have implied that Lilavati was Bhaskaracharya's wife, or even one of his students — raising the possibility that women in parts of the Indian subcontinent could have participated in higher education as early as eight centuries ago. However, given that Bhaskara was a poet and pedagogue, it is also possible that he chose to address his mathematical problems to a doe-eyed girl simply as a whimsical and charming literary device.

A model eliciting framework for integrating mathematics and robotics learning

Robotics is taught in many Australian ICT classrooms, in both primary and secondary schools. Robotics activities, including those developed using the LEGO Mindstorms NXT technology, are mathematics-rich and provide a fertile round for learners to develop and extend their mathematical thinking. However, this context for learning mathematics is often under-exploited. In this paper a variant of the model construction sequence (Lesh, Cramer, Doerr, Post, & Zawojewski, 2003) is proposed, with the purpose of explicitly integrating robotics and mathematics teaching and learning. Lesh et al.’s model construction sequence and the model eliciting activities it embeds were initially researched in primary mathematics classrooms and more recently in university engineering courses. The model construction sequence involves learners working collaboratively upon product-focussed tasks, through which they develop and expose their conceptual understanding. The integrating model proposed in this paper has been used to design and analyse a sequence of activities in an Australian Year 4 classroom. In that sequence more traditional classroom learning was complemented by the programming of LEGO-based robots to ‘act out’ the addition and subtraction of simple fractions (tenths) on a number-line. The framework was found to be useful for planning the sequence of learning and, more importantly, provided the participating teacher with the ability to critically reflect upon robotics technology as a tool to scaffold the learning of mathematics.

Building teachers' pedagogy practices in reasoning, to improve students' dispositions towards mathematics

Drawing on participatory action research, this study identifies the pedagogies necessary to advance reasoning, which is one of the proficiencies from the Australian Curriculum Mathematics, and explores how reasoning leads to greater productive disposition. With the current emphasis on STEM in schools, this research is timely. This thesis makes an original and substantive contribution to the understanding of why and how teachers can most effectively advance student proficiency in reasoning through targeted instructional strategies and style of instruction. The study explores the ways in which teacher practices, when focused on reasoning, enhance the disposition of students towards greater mathematical proficiency.

Mathematics, nature and cryptography: Insights from philosophy of information

One influential image that is popular among scientists is the view that mathematics is the language of nature. The present article discusses another possible way to approach the relation between mathematics and nature, which is by using the idea of information and the conceptual vocabulary of cryptography. This approach allows us to understand the possibility that secrets of nature need not be written in mathematics and yet mathematics is necessary as a cryptographic key to unlock these secrets. Various advantages of such a view are described in this article.

Case study: Digital approaches to English and mathematics

Case study on six partner organisations in the eastern region and how they have supported learners on apprenticeship and traineeship programmes.

An investigation of post-primary students' images of mathematics

This research study investigates the image of mathematics held by 5th-year post-primary students in Ireland. For this study, “image of mathematics” is conceptualized as a mental representation or view of mathematics, presumably constructed as a result of past experiences, mediated through school, parents, peers or society. It is also understood to include attitudes, beliefs, emotions, self-concept and motivation in relation to mathematics. This study explores the image of mathematics held by a sample of 356 5th-year students studying ordinary level mathematics. Students were aged between 15 and 18 years. In addition, this study examines the factors influencing students‟ images of mathematics and the possible reasons for students choosing not to study higher level mathematics for the Leaving Certificate. The design for this study is chiefly explorative. A questionnaire survey was created containing both quantitative and qualitative methods to investigate the research interest. The quantitative aspect incorporated eight pre-established scales to examine students‟ attitudes, beliefs, emotions, self-concept and motivation regarding mathematics. The qualitative element explored students‟ past experiences of mathematics, their causal attributions for success or failure in mathematics and their influences in mathematics. The quantitative and qualitative data was analysed for all students and also for students grouped by gender, prior achievement, type of post-primary school attending, co-educational status of the post-primary school and the attendance of a Project Maths pilot school. Students‟ images of mathematics were seen to be strongly indicated by their attitudes (enjoyment and value), beliefs, motivation, self-concept and anxiety, with each of these elements strongly correlated with each other, particularly self-concept and anxiety. Students‟ current images of mathematics were found to be influenced by their past experiences of mathematics, by their mathematics teachers, parents and peers, and by their prior mathematical achievement. Gender differences occur for students in their images of mathematics, with males having more positive images of mathematics than females and this is most noticeable with regards to anxiety about mathematics. Mathematics anxiety was identified as a possible reason for the low number of students continuing with higher level mathematics for the Leaving Certificate. Some students also expressed low mathematical self-concept with regards to higher level mathematics specifically. Students with low prior achievement in mathematics tended to believe that mathematics requires a natural ability which they do not possess. Rote-learning was found to be common among many students in the sample. The most positive image of mathematics held by students was the “problem-solving image”, with resulting implications for the new Project Maths syllabus in post-primary education. Findings from this research study provide important insights into the image of mathematics held by the sample of Irish post-primary students and make an innovative contribution to mathematics education research. In particular, findings contribute to the current national interest in Ireland in post-primary mathematics education, highlighting issues regarding the low uptake of higher level mathematics for the Leaving Certificate and also making a preliminary comparison between students who took part in the piloting of Project Maths and students who were more recently introduced to the new syllabus. This research study also holds implications for mathematics teachers, parents and the mathematics education community in Ireland, with some suggestions made on improving students‟ images of mathematics.

Politics, Power, PISA: a genealogy of mathematics education policy at second level in Ireland at the beginning of the 21st century

This thesis traces a genealogy of the discourse of mathematics education reform in Ireland at the beginning of the twenty first century at a time when the hegemonic political discourse is that of neoliberalism. It draws on the work of Michel Foucault to identify the network of power relations involved in the development of a single case of curriculum reform – in this case Project Maths. It identifies the construction of an apparatus within the fields of politics, economics and education, the elements of which include institutions like the OECD and the Government, the bureaucracy, expert groups and special interest groups, the media, the school, the State, state assessment and international assessment. Five major themes in educational reform emerge from the analysis: the arrival of neoliberal governance in Ireland; the triumph of human capital theory as the hegemonic educational philosophy here; the dominant role of OECD/PISA and its values in the mathematics education discourse in Ireland; the fetishisation of western scientific knowledge and knowledge as commodity; and the formation of a new kind of subjectivity, namely the subjectivity of the young person as a form of human-capital-to-be. In particular, it provides a critical analysis of the influence of OECD/PISA on the development of mathematics education policy here – especially on Project Maths curriculum, assessment and pedagogy. It unpacks the arguments in favour of curriculum change and lays bare their ideological foundations. This discourse contextualises educational change as occurring within a rapidly changing economic environment where the concept of the State’s economic aspirations and developments in science, technology and communications are reshaping both the focus of business and the demands being put on education. Within this discourse, education is to be repurposed and its consequences measured against the paradigm of the Knowledge Economy – usually characterised as the inevitable or necessary future of a carefully defined present.

Analyzing and selecting tasks for mathematics teaching: a heuristic

In planning units and lessons every day, teachers face the problem of designing a sequence of activities to promote learning. In particular, they are expected to foster the development of learning goals in their students. Based on the idea of learning path of a task, we describe a heuristic procedure to enable teachers to characterize a learning goal in terms of its cognitive requirements and to analyze and select tasks based on this characterization. We then present an example of how a group of future teachers used this heuristic in a preservice teachers training course and discuss its contributions and constraints.